Application of the Wavelet Transform with a Piecewise Linear Basis to the Evaluation of the Hankel Transform
Numerical Analysis
2007-05-23 v1 Mathematical Physics
math.MP
Abstract
A method for computing the Hankel transform is proposed whereby the letter is reduced to a sum by representing the integrand as a smooth function times a Bessel function. The smooth function is replaced by its wavelet decomposition with a basis such that its scalar product with the Bessel function is calculated analytically. The result is represented as a series, with the coefficients strongly depending on the local behavior of the function being transformed. The application of the method is demonstrated by an example illustrated with plots.
Keywords
Cite
@article{arxiv.math/0406263,
title = {Application of the Wavelet Transform with a Piecewise Linear Basis to the Evaluation of the Hankel Transform},
author = {P. S. Zykov and E. B. Postnikov},
journal= {arXiv preprint arXiv:math/0406263},
year = {2007}
}